Cecil Moore wrote:
Please apply the same irradiance equation that
optical physicists were using before you were born.
Any physics professor should be able to accomplish
that simple task. If optical physicists were in
error in using that equation 100 years ago, please
explain their error.

So far no response to this simple request. The
graphic of the non-reflected glass example is
at http://www.w5dxp.com/thinfilm.gif

We know that the reflections are 100% canceled
during steady-state.

The problem is: With the given data, calculate
the magnitude of the total reflection back toward
the source immediately after the first internal
reflection arrives back at the thin-film to air
surface at time t3 and is superposed with the
external reflection. The two superposed waves are
180 degrees apart.

The external reflection is 0.01 watts at a reference
angle of zero deg. This is the normal reflection
from the thin-film surface

The first internal reflection is 0.009801 watts
at 180 degrees. This is the first reflection from
the glass.

These two waves superpose at t3. The irradiance
equation, using P for power density, is:

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

where (A) is the angle between the two waves and
Ptotal is the total power density of the reflections
toward the source after the two waves are superposed.

Ptotal = 0.01 + 0.009801 + 2*SQRT(0.01*0.009801)(-1)

Ptotal = 0.019801 - 0.0198 = 0.000001 watt

There is 0.0198 watts of destructive interference
which, according to the conservation of energy
principle, must result in 0.0198 watts of
constructive interference in the opposite direction.

The magnitude of the reflection toward the source
drops from 0.01 watt to 0.000001 watt at the arrival
of the first internal reflection from the glass. That's
a five magnitude reduction in the reflections at the
time of the arrival of the first internal reflection.
The reflections back toward the source are eventually
completely eliminated during steady-state.

There was no vector math and no need to calculate
the magnitudes and phases of the electric and magnetic
fields - just a straight forward calculation to get
the answer.

As long as the source remains in place, the steady-
state cancellation of the reflections toward the source
is permanent. It is difficult to analyze how that could
happen unless the internal reflections interact with the
external reflection resulting in wave cancellation.

Everyone is invited to prove the above calculation to
be incorrect. Hint: if one actually performs a vector
analysis, the magnitude of reflection result will be
exactly the same as above.

The above method does not invalidate or replace a vector
analysis. Unlike a vector analysis, it simply shows where
the energy goes. Optical physicists knew this a century
ago - most RF engineers have yet to learn it.
--
73, Cecil http://www.w5dxp.com